Quasi-long-range ordering in a finite-size 2D Heisenberg model

Oleksandr Kapikranian (1, 2) , Bertrand Berche (2) , Yurij Holovatch (1, 3)

1 ICMP - Institute for Condensed Matter Physics of NAS of Ukraine
2 LPM - Laboratoire de physique des matériaux
3 Institut für Theoretische Physik

We analyse the low-temperature behaviour of the Heisenberg model on a two-dimensional lattice of finite size. Presence of a residual magnetisation in a finite-size system enables us to use the spin wave approximation, which is known to give reliable results for the XY model at low temperatures T. For the system considered, we find that the spin-spin correlation function decays as 1/r^eta(T) for large separations r bringing about presence of a quasi-long-range ordering. We give analytic estimates for the exponent eta(T) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.

Mots clés: Heisenberg model; quasi-long-range ordering; spin-wave approximation; Monte Carlo simulations

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique des Hautes Energies - Réseau [hep-lat]; Mécanique statistique [cond-mat.stat-mech]

Oleksandr Kapikranian, Bertrand Berche, Yurij Holovatch. Quasi-long-range ordering in a finite-size 2D Heisenberg model. 2006. ⟨hal-00115964⟩